iphone won't automatically re-connect to wi-fi; have to re-enter password each time

I just "upgraded" my wi-fi router to a Netgear WNDR3400. Everything seems to be set up fine, and I'm able to connect with our various iphones, ipads, and AppleTV. But our iphones won't automatically re-connect to the network after the connection is lost, and we have to re-enter the password when we re-connect.

The computer doesn't have a problem re-connecting, and doesn't keep asking for the password.

I've posted to the Apple forum, but I think the problem may be with the router/set-up, since this wasn't a problem with my older Netgear router.